From Rayleigh-Bérnard convection to atmospheric vertical vortices

By Henar Herrero (Universidad de Castilla-La Mancha), in collaboration with Damián Castaño y María Cruz Navarro.

There are different atmospheric phenomena with the common factor of vortex dynamics, from small events such as dust devils (figure 1) and tornadoes, to large events as hurricanes and cyclones [4,5]. Thermal convection is a relevant process involved in their formation and evolution. In thermal convection, the fluid motion is caused by buoyancy forces that results from the density variations due to thermal gradients in the fluid. The simplest case of thermal convection is the well-known Rayleigh Bénard convection where cells or rolls appears in a horizontal fluid layer heated from below [1]. Instability occurs at the minimum temperature gradient at which a balance can be steadily maintained between the kinetic energy dissipated by viscosity and the internal energy released by the buoyancy flow [3]. One of the hypothesis for the genesis of these atmospheric vortices is thermoconvective instability in a stratified layer. Many questions from different fields need to be solved, from the physical model to the numerical methods to solve the differential equations (figure 2) [2].

 

Figure 1. Left: real dust devil; right: numerical vertical vortex

DDEqs

Figure 2. Model equations

 

References

[1]  Bénard H. Les tourbillons cellulaires dans une nappe liquide. Rev. Gén. Sci. Pure Appl. 11, 1261-1271, 1900.                                                                                                                                            

[2] Castaño, D., Navarro, M. C. and Herrero, H. Routes to chaos from axisymmetric vertical vortices in a rotating cylinder. Mathematical Modelling. doi: 10.1016/j.apm.2017.09.010, 2017.                                                 

[3]  Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability. Dover Publications, New York, 1981.          

[4]  Emanuel K. A. Divine wind. Nature. Oxford University Press, Oxford, 2005.

[5] Sinclair P. C. General characteristics of dust devils. J. Appl. Meteorol. 8, 32-45, 1969.

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